Hi, This is a question about accepting/rejecting hypothesis, could you please ex

Question

Hi,

This is a question about accepting/rejecting hypothesis, could you please explain and solve this problem, thank you.

PS: The red text is the answer

Problem 1: Binomial Distribution We wish to test the hypothesis that data is being generated by the binomial process binom(500,0.4) Given the datum value 195, we accept that it is generated by the process if it is in a 95% symmetric about the mean interval for the process. Using a normal approximation, we accept the hypothesis if the datum is and at most U Since 195 (pick one n the interval, pick one) the hypothesis. CHECK L 178.5297 and U 221.4703 195 is in the interval We accept the hypothesis.

Explanation / Answer

Solving question1,

n = 500

p = 0.4

q = 1-p=0.6

mean = np = 200

standard deviation = sqrt(npq) = sqrt(50080.4*0.6)=10.95

z for 95 confidence interval is 1.96

Hence, the interval is (mean-z*standard deviation,mean+z*standard deviation) = (200-1.96*10.95,200+1.96*10.95) = (178.52,221.47) . Since, 195 lies in the confidence interval, we accept the hypothesis.

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